Answer:
00.5 is a answer A IS A ANSWER
The length of an edge is the cubic root of the volume.
Cubic root 1.8 = 1.2 meters
Answer:
D) (x, y) → (1/3x , 1/3 y)
Step-by-step explanation:
A dilation is a change of size, if the dilation factor is greater than 1, then the figure is enlarged. If the dilation factor is smaller than 1, the figure is shrinked. In both cases, the coordinates are MULTIPLIED by the dilation factor.
Among the 4 choices, only 2 are dilations. One is with a dilation factor of 3 (A), which means the shape was enlarged. And the other is with dilation factor of 1/3, meaning the shape was shrinked.
Since we went from MNOP (LARGE one) to M'N'O'P' (small one), the dilation factor was < 1... so 1/3 is the answer.
Answers B and C show a translation/movement of the shape, not a dilation.
Last one 7 and 3
9(7)+20(3)>120
63+ 60
123>120
Says 123 minutes is longer than 120 that's why it is that answer
If you start with a 12x16 rectangle and cut square with side length x, when you bend the sides you'll have an inner rectangle with sides
and
, and a height of x.
So, the volume will be given by the product of the dimensions, i.e.
![(12-2x)(16-2x)x = 4x^3-56x^2+192x](https://tex.z-dn.net/?f=%2812-2x%29%2816-2x%29x%20%3D%204x%5E3-56x%5E2%2B192x)
The derivative of this function is
![12x^2-112x+192](https://tex.z-dn.net/?f=12x%5E2-112x%2B192)
and it equals zero if and only if
![12x^2-112x+192=0 \iff x = \dfrac{14\pm 2\sqrt{13}}{3}](https://tex.z-dn.net/?f=12x%5E2-112x%2B192%3D0%20%5Ciff%20x%20%3D%20%5Cdfrac%7B14%5Cpm%202%5Csqrt%7B13%7D%7D%7B3%7D)
If we evaluate the volume function at these points, we have
![f\left(\dfrac{14-2\sqrt{13}}{3}\right) = \dfrac{64}{27}(35+13\sqrt{13})> f\left(\dfrac{14-2\sqrt{13}}{3}\right) = -\dfrac{64}{27}(13\sqrt{13}-35)](https://tex.z-dn.net/?f=f%5Cleft%28%5Cdfrac%7B14-2%5Csqrt%7B13%7D%7D%7B3%7D%5Cright%29%20%3D%20%5Cdfrac%7B64%7D%7B27%7D%2835%2B13%5Csqrt%7B13%7D%29%3E%20f%5Cleft%28%5Cdfrac%7B14-2%5Csqrt%7B13%7D%7D%7B3%7D%5Cright%29%20%3D%20-%5Cdfrac%7B64%7D%7B27%7D%2813%5Csqrt%7B13%7D-35%29)
So, the maximum volume is given if you cut a square with side length
![x=\dfrac{14-2\sqrt{13}}{3}\approx 2.7](https://tex.z-dn.net/?f=x%3D%5Cdfrac%7B14-2%5Csqrt%7B13%7D%7D%7B3%7D%5Capprox%202.7)